A corner_pump method for high_power quasi_three_level lasers is reported. The de sign uses a slab laser configuration with the incident pump light from the slab corner. We present an analytic description of pumping absorption, pumping bright ness, doping concentration and crystal dimension for the corner_pumped composite Yb:YAG laser. In the experiments a maximum continuous-wave output power of 400 W with slope efficiency 28% was achieved. This result shows the validity of corn er_pumping concept and its feasibility in the development of high_power solid_st ate lasers.